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1.1 Inductive Reasoning MGF1106 Terms those are helpful in this section: Natural numbers‐ Whole Numbers: Ellipsis ‐ . . . continues in the same pattern Divisible ‐ if a b has a remainder of 0, then a “is divisible by “b. Even vs. Odd Inductive Reasoning ‐ Ex.1) Add 2 odd Numbers together. Using inductive reasoning, what is your conjecture? Ex.2) Pick 4 consecutive integers. Multiply the first and fourth number together. Multiply the 2nd and 3rd number together. Subtract the first product from the second. What is your conjecture? One way to prove a conjecture is false is by a ___________________________________, which satisfies the conditions of the conjecture, but gives a different result. Find a counter‐example to the conjecture “an even number times an even number is odd.” __________ Not all conclusions found by inductive reasoning are correct. We made a conjecture using inductive reasoning. To PROVE – use deductive reasoning. Deductive Reasoning ‐ Back to ex 1 and 2) Ex.1) Add 2 odd Numbers together. Using deductive reasoning, to prove your conjecture? Ex.2) Pick 4 consecutive integers. Multiply the first and fourth number together. Multiply the 2nd and 3rd number together. Subtract the first product from the second. Using deductive reasoning, to prove your conjecture? Pg 6 in the book: Use inductive reasoning to predict the next number in the pattern. 20. 3, 7, 11, 15…… 24. 4, ‐20, 100, ‐500 ….. 26. 0, 1, 3, 6, 10, 15… 27 81 , 64 ,... 28. 3, 94 , 16 40. Pick any number and multiply the number by 4. Add 6 to the product. Divide the sum by 2 and subtract 3 from the quotient. a‐c) use inductive reasoning to find a conjecture. d) Try to prove, using deductive reasoning. 44. Find a counterexample to show that the following statement is incorrect. The quotient of any two counting numbers is a counting number.